Pole-Tide Modulation of Slow Slip Events at Circum-Pacific

Bulletin of the Seismological Society of America, Vol. 95, No. 5, pp. 2009–2015, October 2005, doi: 10.1785/0120050020

Pole-Tide Modulation of Slow Slip Events at Circum-Paciﬁc Subduction Zones by Zheng-Kang Shen, Qingliang Wang, Roland Bu¨rgmann, Yongge Wan, and Jieyuan Ning

Abstract Episodic slow slip (ESS) events have been detected at several circum- Pacific subduction zones, such as Cascadia, Japan, and Mexico. Notably, at least eight ESS events along the northern Cascadia subduction zone recurred with a period of 13–16 months. We study the relationship between pole-tide (associated with Chan- dler wobble with a period of ϳ14 months)-induced stress and the occurrence of the ESS events. Our quantitative analysis shows that 14 of the 20 documented ESS events occurred during the ascension phase, prior to the maximum, of a pole-tide-induced Coulomb failure stress change, and three events occurred at the stress-change peak. The pole tides modulate the stress field at the downdip edge of the transition zone along the plate interface and may trigger ESS events when conditions are favorable. The phase advance of the triggered events with respect to the induced Coulomb failure stress change may reflect that the fault slip is dictated by a rate- and state- dependent friction law inferred from laboratory experiments.

Introduction

Slow slip events have been observed around the circum- More ESS events have been discovered at other circum- Pacific subduction zones, and some are found to recur almost Pacific subduction zones such as along the Japanese islands periodically. The most remarkable example of such repeat- and at Guerrero, Mexico. Two transient slip events were ing ESS events is found at the northern Cascadia subduction captured by a continuous GPS network off Bungo Channel, zone (Dragert et al., 2001; Miller et al., 2002; Rogers and Japan, in 1996–1997 and 2003, respectively (Hirose et al., Dragert, 2003). Since 1993, eight ESS events have been de- 1999; Miyazaki et al., 2003; Ozawa et al., 2004). The 1996– tected by continuous Global Positioning System (GPS) mea- 1997 event lasted for about a year, from November 1996 to surements in the vicinity of Vancouver Island, British Co- November 1997. The event had a gentle start, and acceler- lombia, where stations were found to reverse their motion ated later from July to November 1997. The 2003 event took directions with respect to the interior of the North American place from July 2003 to February 2004, with most of the plate for 1–3 weeks every 13 to 16 months (Dragert et al., deformation accumulated between August and November 2001) (Fig. 1). Emissions of tremor-like seismic signals were 2003 (Ozawa et al., 2004). Low-frequency tremors were also subsequently discovered accompanying such slip events recorded during this time period, mostly between 1 Septem- (Rogers and Dragert, 2003). Recently, slow slip and tremor ber and 1 December 2003, coinciding with the time period events have also been reported at the southern Cascadia sub- when most of the transient slip was taking place (Ozawa et duction zone. Eight ESS events were detected by a contin- al., 2004). Modeling of the GPS displacement data placed uous GPS station located near the California/Oregon border the sources of the two slip events at the same segment of the 1997–2004, with seismic tremors observed accompanying slab interface between the Eurasian plate and the subducting the last five events (Szeliga et al., 2004). At the northwestern Philippine Sea plate (Ozawa et al., 2004). The tremors were tip of Vancouver Island seismic tremor events were ob- found to occur at the downdip edge of the slip area, and served, with a 6-month phase lag behind the south island likely spurred subsequent, more rapid, updip slip (Ozawa et events (Dragert et al., 2004). Modeling of GPS-observed ep- al., 2004). Obara et al., (2004) reported more tremor events isodic displacements has placed the source of such ESS in the region between January 2001 and December 2003, events near the downdip edge of the coupled plate interface, with a recurrence period of around 6 months. They also ob- at 25–45 km depth (Dragert et al., 2001), downdip of the served tilt changes concurrently with these events. Most of seismogenic zone of the megathrust, which is shallow and these events, however, lasted only a few days and would mostly offshore (Wang et al., 2003). The total slip for each result in surface displacement no more than 2 mm (Obara et ESS event is about 2–4 cm, with the seismic moment release al., 2004). Consequently, no slow slip was observed by GPS equivalent to an M ϳ 6.5 earthquake (Dragert et al., 2004). concurrently with these events, except for the one that oc-

2009 2010 Short Notes

Figure 1. Schematic view of tectonic setting of subduction zone and occurrence of ESS events. Large open arrows mark the secular motion of the oceanic plate relative to the continental plate, with the relative motion across the plate interface shown by open arrows. The small open arrow next to the GPS antenna points to its secular motion direction with re- gard to the interior of the continental plate. Solid arrows on the plate interface show the episodic slow slip events that occurred in the locked-to-creeping transition zone, with their associated surface motion direction indicated by a solid arrow next to the GPS antenna.

curred late 2003, and we consider these events to be minor, tection of two more slow slip events that occurred since with mechanisms that differ from what we discuss here. 2002; one occurred around the beginning of 2003, and the About 700 km east-northeast from the Bungo Channel, other started in January 2004. Additional slow slip events two transient events took place around the Boso Peninsula may have occurred in 1999, 2000, and 2001, some of which in 1996 and 2002 and were recorded by the GEONET GPS might be associated with preceding seismic events (DeMets network (Ozawa et al., 2002, 2003). The 1996 event oc- et al., 2004). Similar to the Cascadia and Japanese island curred for perhaps more than a year, but most of the transient events, these Guerrero events are believed to have occurred slip took place from 8 April to 10 June 1996 (Ozawa et al., at the transition zone of the subducting plate interface, about 2002), or 16 May to 23 May 1996 (Sagiya, 2004). The 2002 60–180 km landward from the trench. Equivalent seismic event lasted for about 50 days from 4 October to 2 December moments released for the 1998, 2002, and 2003 events are

(Ozawa et al., 2003). The two events show similar defor- on the order of Mw 7.2, Mw 7.4, and Mw 7.2 earthquakes, mation patterns: centimeter-level surface displacement in the respectively, based on geodetic deformation modeling southeast direction with respect to the interior of the Japa- (Lowry et al., 2004). In this article, we examine only the nese islands (Ozawa et al., 2002, 2003), except that a recent events of 1998 and 2002, since we do not know precise study showed that surface motion of the 1996 event was timings and durations of the other events yet. more southward, rather than parallel to the relative plate mo- Although these ESS events have been documented and tion direction (Sagiya, 2004). Modeling of the displacement their mechanical processes have been hypothesized, little is field placed the source of deformation at the upper surface known about what triggers them. Miller et al. (2002) pointed of the subducting Philippine Sea plate off the Boso Peninsula out a remarkable correlation between the periods of the Cas- (Ozawa et al., 2002). Low-frequency seismic activity was cadia ESS recurrences and Chandler wobble (the latter refers also observed during these two time periods (Ozawa et al., to wobbling of the Earth’s rotation pole around its inertia 2003). Another slow slip event was recorded in the Tokai figure, caused by mass movement of the Earth) (Melchior, area, starting as early as July 2000 through at least June 1978): both are about 14.5 months. However, they dismissed 2002. This event was possibly triggered by a swarm of the latter as a plausible triggering source on the grounds of seismo-volcanic activities around the Izu Islands from July the small stress perturbation it may generate. But how much to September 2000 (Ozawa et al., 2002). Because of its and of what phase is the stress change induced by the Chan- unique triggering mechanism and long duration, it is not dler wobble, and can that, after all, trigger the ESS events? included in this analysis; however, the initiation of the event apparently occurred during ascending pole-tide stress. Two slow slip events have been reported at the Guerrero The Model subduction zone, Mexico, between the Cocos and North America plate (Lowry et al., 2001; Kostoglodov et al., To answer these questions we calculate the stress 2003). The first event occurred between December 1997 and change produced by the pole tide at the locked-to-creeping June 1998, with ϳ3-cm reversed displacement accumulated transition zone interface at the subduction zones mentioned at a continuous GPS station. The second event took place above, which are subsequently transformed to a coordinate from October 2001 to May 2002, with up to ϳ7 cm of anom- system referenced to the plate interface. Gravitational poten- alous displacement accumulated at some GPS sites during tial induced by variation of Earth rotation can be expressed this time period. Recently, Lowry et al. (2004) reported de- as (Wahr, 1985): Short Notes 2011

1 The free surface boundary condition provides us with 3 more X22r [sin 2h(m cos k מס (V(h,k 2 0 x equations: 2 ם ם myzsin k) 2m sin h] ס ס ס srr shr skr 0 where h and k are colatitude and longitude respectively; X0 is the Earth’s rotation rate, r the position radius, mx and my Assuming elastic media, we can combine the above are the vector components of the rotation pole change and equations for the three known stress and three known strain can be obtained from the International Earth Rotation and components and their constitutive relationships to derive the Reference System server (IERS, www.iers.org/iers/products/ other three stress components shh, skk, and shk. To a first- eop), and mz is the change of rotation rate, which is an order order approximation, we assume that the pole-tide-induced of magnitude smaller than mx and my. Pole-tide-induced dis- stress does not vary with depth within the shallow depth placement at the Earth’s surface, given by Wahr (1985) and (tens of kilometers) of the Earth. The above equations then Gipson and Ma (1998) is: are used to evaluate the Coulomb stress change induced by the pole tide. 22 h X0 r h [sin 2h(m cos kמס (V(h,k,m ס U rxg 2g Results [2m sin2 h ם (m sin k ם yz We choose the Coulomb stress estimation spot to be located near the downdip end of the transition zone from ץ l 1 fully locked to creeping following published estimates. The ס Uk V(h,k,m) -k plate geometry parameters are listed in Table 1. The calcuץ g sinh 22 X0 r lated pole tide induced stresses on the plate interface for all (m cos k מ l cos h(m sin k ס g xythe areas are shown in Figure 2. A remarkable synchroni- zation is evident between the occurrences of the ESS events and phases of pole-tide-induced updip shear stress . Most 22 ץ l X0 r s l [cos 2h(m cos kמס (V(h,k,m ס U ,h g x of the recorded ESS events occurred during ascension of sץ h g m sin 2h] and some of them were close to or at the maximum of s.It ם (m sin k ם yzis also noted, however, that the pole-tide-induced normal stress r oscillates with a phase offset of ϳ180Њ from s; that where l and h are Love numbers, given as l Ϸ 0.085 and is, the slip events occurred when pole-tide stresses further h Ϸ 0.600; g is the gravitational constant. compressed the fault plane. If we assume a friction coeffi- We derive pole-tide-induced strains of three compo- the static Coulomb failure stress change ,0.4 ס cient of l nents from above equations: lr is a bit smaller than but still synchronized ם s ס DCFS with . For the 20 slow slip events recorded at the five sub- s 2 ץ 1 UUr X0 r -h l m duction zones described above, 14 occurred during the asסםס sin 2h( x cos k] 2 ץ ehh r h rg cension phase, three at the maximum, and three in the de- X2 r scending phase of the pole-tide-induced Coulomb failure h 0מ [m cos 2h מ (m sin k ם yz 2g stress change. Among the three events that slipped during the descending phase, two were in southern Cascadia and 2 ם ם [sin 2h(mxycos k m sin k) 2m zsin h] one was at the Boso Peninsula of southwest Japan. It should be noted that the elasticity assumption used ץ 1 UU Ur for stress and deformation estimation above is valid only for ם khctghםס e ,k rr the region outside of the fault zone. Within the fault zoneץ kk r sin h 2 the effect of fault creep downdip from the transition zone ם מ X0 r ס lctgh[(1 cos 2h)(mxycos k m sin k) should be accounted for. A qualitative model suggests that g such an effect may amplify the Coulomb failure stress on מ mz sin 2h] the locked plate interface by an order of magnitude. This test is done using a finite-element model, assuming a subducting X2 r slab dipping at 30Њ, with the slab interface completely locked 2 ם ם 0 מ h [sin 2h(mxycosk m sink) 2m zsin h] 2g from 0 to 40 km depth, and bearing no shear stress at Ͼ40 km depth (for time periods of several months, within UU which the locked-to-creeping transition zone is assumedץU 1ץ11 ΂΃hkkctghמםס e h r with no episodic slipping). The result shows a 5- to 65-foldץ k rץ hk 2 r sin h increase of the induced shear stress changes around the tran- 2 sition zone of the subducting plate at 25–40 km depth. A מ X0 r מס l sin h(mxysin k m cos k) g smoothly tapered fault strength of the transition zone would 2012 Short Notes

Table 1 Parameters of Subduction Zone Plate Setting and Locations of Stress Evaluation

Segment Strike Dip Rake Latitude Longitude Reference

N. Cascadia N30ЊW20Њ 90Њ 48.4ЊN 123.5ЊW Wang et al., 2001 S. Cascadia N5ЊW20Њ 90Њ 41.8ЊN 122.7ЊW Szeliga et al., 2004 Guerrero N70ЊW20Њ 80Њ 17ЊN99ЊW Kostoglodov et al., 2003 Bungo Channel N20ЊE20Њ 70Њ 32ЊN 132ЊE Miyazaki and Heki, 2001 Boso Peninsula N25ЊE20Њ 80Њ 35ЊN 141.5ЊE Ozawa et al., 2003 reduce the stress amplification at its lower end, but would terich, 1981; Ruina, 1983). The triggering effect can depend increase the amplification at its upper end. Thus it is reason- strongly on the oscillation period of the modulation stress. able to expect the pole-tide-induced Coulomb stress changes Laboratory experiments of a fault system loaded by a com- at the transition zone to be at the level of 1 kPa or above. bination of steady stressing and a low-frequency oscillatory loading indicate that when the period of the sinusoidal stress Discussion and Conclusions is long enough (hundreds of seconds, presumably much longer than the nucleation time of cracks), the triggering Can pole-tide-induced stress change be large enough to threshold for stress oscillation is significantly reduced (Bee- trigger ESS? This question is not easy to answer, because of ler and Lockner, 2003). “Earthquakes” could be triggered our lack of knowledge of most of the relevant factors, such even if the amplitude of the periodic loading is about one as the tectonic stress/strain rate and state, slip (or slow earth- order of magnitude smaller than the accumulated loading quake) nucleation time, and the appropriate constitutive law stress in an oscillation cycle. Beeler and Lockner (2003) at the transition zone of the subducting plate interface. How- estimated the minimum duration of earthquake nucleation ever, recent geophysical studies have provided some clues. on major fault zones as ϳ1 year. This may suggest that the One of them is the observation of earthquake triggering un- triggering threshold for periodic loading stress at the inter- der extreme solid Earth tides. The solid Earth tides cause mediate (months to years) timescale could be much less than daily stress oscillation in the crust, on the order of several that at the short-immediate (hours to days) timescale. That kPa. Previous statistical studies of Vidale et al. (1998) found is, pole-tide-induced Coulomb stress may be able to trigger virtually no triggering of microseismicity from solid Earth ESS at the intermediate timescale (ϳ102 days), while the tides. Their recent study (Cochran et al., 2004), however, larger diurnal and semidiurnal Earth tides rarely do. showed that in the subset of earthquakes that occurred during Beeler and Lockner (2003) find in their laboratory ex- the top 1% of absolute Earth-tide-induced Coulomb stress periments that under the combined action of a constant stress (Ն ϳ10 kPa), 74% of the events occurred when Coulomb loading and a small sinusoidal stress, there is a phase shift stress was positive, suggesting that the triggering effect is between fault slip events and peak periodic loading stress. significant (Ͼ99% confidence). Such a result suggests that If the stress oscillation period is longer than the duration of for short-term triggering of earthquakes, Coulomb stress in- slip nucleation, slip may take place before the system duced by diurnal and semidiurnal tides (on the order of reaches the maximum of the periodic loading stress. This is 1 kPa) are normally just below the triggering threshold; they consistent with our observation that ESS events almost al- could, however, play a triggering role when they are at their ways occur before the maximum pole-tide-induced Coulomb extremes. Such an assessment is corroborated by the study stress change. of Tanaka et al. (2004), who discovered that tidal triggering If pole-tide-induced Coulomb stress is capable of trig- may be significant in a small fraction of the subduction zone gering ESS events, what about other periodic loading forces regions in Japan, where directions of tidal-induced com- caused by motions of solid or fluid objects? Murakami and pressional stress at the time of the earthquakes is strongly Miyazaki (2001) reported seasonal variation of crustal de- correlated with the compressional P axes of observed earth- formation measured by a continuous GPS network within the quakes (Stein, 2004). Japanese island arc. Heki (2001) linked the annual surface If stress induced by the extreme solid Earth tides could displacements to heavy snow loading in northeast Japan. He barely play a seismic triggering role, what about the pole- estimated that the periodic loading of snow could be equiv- tide-induced stress changes, which are estimated to be on the alent to up to 10 kPa atmospheric pressure change. Interest- order of 1 kPa, smaller than the interseismic stress build-up ingly enough, seasonality of earthquake occurrence has also during a pole-tide oscillation cycle (Mazzotti and Adams, been observed and related to crustal deformation in Japan 2004). The pole tide oscillates at a much lower frequency, (Ohtake and Nakahara, 1999). Although the snow loading and ESS events occur at the plate interface of different depth region is hundreds of kilometers away from the subduction range and fault rheology than ordinary earthquakes. The zone, it may still cause a Coulomb stress change at the plate faulting process there is determined not only by its static interface on the order of hundreds of Pa (Heki, 2001), similar stress state, but also by deformation rate and history (Die- to the pole-tide-induced Coulomb stress. An ESS event, Short Notes 2013

Figure 2. Pole-tide-induced stress-change time series. Solid curve is the Coulomb failure stress change on the slab interface, dashed and dotted curves are its shear and normal components, respectively. Fault normal tension and thrust-sense shear stress are positive. Gray vertical stripes are the epochs of the ESS events. (a) northern Cas- cadia, (b) southern Cascadia, (c) Guerrero, (d) Bungo Channel, and (e) Boso Peninsula subduction zones. Gray curve in (a) is the Coulomb failure stress change induced by annual and semiannual Earth tides. which our model cannot fit, at Boso Peninsula from April to The occurrence of seismic tremor associated with ESS June 1996, was in phase with the snow loading-induced suggests active involvement of fluids that may be released Coulomb stress at the interface of the subduction zone (Heki, in slab dehydration reactions (Rogers and Dragert, 2003; 2001). This may be more than a coincidence. The high- Szeliga et al., 2004). Presence of pressurized fluids at the frequency diurnal and semidiurnal tides, as discussed above, transition zone may lubricate the plate interface and reduce do not appear to play a strong triggering role. Amplitudes the triggering threshold substantially. Gao et al. (2000) dis- of the monthly and semimonthly Earth tides are slightly covered that triggered miscoseismicity in hydrothermal or larger than that of the semiannual Earth tide, but their pe- volcanic regions in the western United States was modulated riods are perhaps still too short to impose a sustained stress by an annual cycle within 5 years following the 1992 Land- for triggering. The annual and semiannual Earth tides, as ers earthquake. They interpreted the periodic seismicity fluc- shown in Figure 2, have much smaller magnitudes than the tuation as caused by barometric pressure change, which has pole tide (Melchior, 1978), and do not appear to be signifi- an annual magnitude of only about 2 kPa. No such annual cant in earthquake or ESS triggering. Annual barometric cycle, however, was found for microearthquakes that oc- pressure change would be less than 1 kPa at the depths (25– curred in other regions without hydrothermal or volcanic 45 km) we are investigating. Other potential oscillatory load- origin, suggesting that presence of a fluid phase in the crust ing sources, such as tidal and nontidal ocean loading, con- could make a difference in earthquake triggering. Another tribute most at coastal sites such as those around Vancouver study by Custodio et al. (2003) discovered strong M2 Earth Island, but still less than that of the solid Earth tides, and tide modulation of volcanic tremors at Fogo Volcano, Cape can be ignored (Scherneck, 1991). Verde, again suggesting the exceptional sensitivity of trig- 2014 Short Notes gering in the presence of geophysical fluids. Neuberg (2000) work presented here may provide a viable scenario for future also reported numerous cases of strong correlation between theoretical and modeling studies to investigate. seismo-volcanic activities and periodic loading forces such as the diurnal and semidiurnal tides and barometric pressure Acknowledgments change in Italy, New Zealand, and Indonesia. Along the Nankai subduction zones, Kodaira et al. (2004) discovered We are grateful to Herb Dragert, Garry Rogers, Tim Melbourne, Nick a high Poisson’s ratio at the subducting plate interface based Beeler, and Dave Jackson for discussions and comments. Kelin Wang’s on seismic V /V imaging, and suggested that presence of review also helped improve the manuscript. This work was supported by p s grants from the Natural Science Foundation of China (40334042) and NSF fluid might lower the triggering threshold substantially for (EAR-0409902). the occurrence of slow slip events there. 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